Question: Solve for $x$ and $y$ using elimination. ${-3x-3y = -45}$ ${2x-4y = -6}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $3$ ${-6x-6y = -90}$ $6x-12y = -18$ Add the top and bottom equations together. $-18y = -108$ $\dfrac{-18y}{{-18}} = \dfrac{-108}{{-18}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-3x-3y = -45}\thinspace$ to find $x$ ${-3x - 3}{(6)}{= -45}$ $-3x-18 = -45$ $-3x-18{+18} = -45{+18}$ $-3x = -27$ $\dfrac{-3x}{{-3}} = \dfrac{-27}{{-3}}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {2x-4y = -6}\thinspace$ and get the same answer for $x$ : ${2x - 4}{(6)}{= -6}$ ${x = 9}$